Detection and Estimation of Diffuse Signal Components Using the Periodogram

Abstract

One basic limitation of using the periodogram as a frequency estimator is that any of its significant peaks may result from a diffuse (or spread) frequency component rather than a pure one. Diffuse components are common in applications such as channel estimation, in which a given periodogram peak reveals the presence of a complex multipath distribution (unresolvable propagation paths or diffuse scattering, for example). We present a method to detect the presence of a diffuse component in a given peak based on analyzing the projection of the data vector onto the span of the signature’s derivatives up to a given order. Fundamentally, a diffuse component is detected if the energy in the derivatives’ subspace is too high at the peak’s frequency, and its spread is estimated as the ratio between this last energy and the peak’s energy. The method is based on exploiting the signature’s Vandermonde structure through the properties of discrete Chebyshev polynomials. We also present an efficient numerical procedure for computing the data component in the derivatives’ span based on barycentric interpolation. The paper contains a numerical assessment of the proposed estimator and detector.

Keywords

• periodogram
• beamformer
• maximum likelihood estimation
• diffuse components
• discrete Chebyshev polynomials
• frequency estimation